我一直在尝试实现逆 DFT(不使用 FFT),但在数学上有点挣扎。从我阅读的实现和伪代码中,我无法弄清楚我的实现存在的问题。
'''
spectrum.clear();
spectrum.add(new ComplexNumber(36.0,0.0));
spectrum.add(new ComplexNumber(-4.000000000000002,9.65685424949238));
spectrum.add(new ComplexNumber(-4.000000000000002,3.9999999999999987));
spectrum.add(new ComplexNumber(-4.0,1.6568542494923788));
spectrum.add(new ComplexNumber(-4.0,0.0));
spectrum.add(new ComplexNumber(-3.999999999999999,-1.656854249492381));
spectrum.add(new ComplexNumber(-3.999999999999998,-4.000000000000001));
spectrum.add(new ComplexNumber(-3.999999999999995,-9.65685424949238));
int N = spectrum.size();
double twoPiOnN = 2 * Math.PI / N;
for(ComplexNumber c : spectrum) {
waveform.add(0.0);
}
double twoPikOnN, twoPijkOnN;
for(int k=0; k<N; k++) {
twoPikOnN = twoPiOnN *k;
for(int j = 0; j < N; j++) {
twoPijkOnN = twoPikOnN * j;
double d = waveform.get(k);
d += spectrum.get(j).getRe() * Math.cos(twoPijkOnN ) - spectrum.get(j).getIm() * Math.sin(twoPijkOnN );
waveform.set(k,d);
}
}
for(Double d : waveform) {
System.out.println(d);
}
''' 这种情况应该导致 [1 ,2 ,3 ,4 ,5 ,6 ,7 ,8] 的波形数组列表。
非常感谢任何帮助。